Problem: Divide the following complex numbers: $\dfrac{12 e^{5\pi i / 4}}{4 e^{2\pi i / 3}}$ (The dividend is plotted in blue and the divisor in plotted in green. Your current answer will be plotted orange.)
Explanation: Dividing complex numbers in polar forms can be done by dividing the radii and subtracting the angles. The first number ( $12 e^{5\pi i / 4}$ ) has angle $\frac{5}{4}\pi$ and radius 12. The second number ( $4 e^{2\pi i / 3}$ ) has angle $\frac{2}{3}\pi$ and radius 4. The radius of the result will be $\frac{12}{4}$ , which is 3. The angle of the result is $\frac{5}{4}\pi - \frac{2}{3}\pi = \frac{7}{12}\pi$ The radius of the result is $3$ and the angle of the result is $\frac{7}{12}\pi$.